Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 5x + 1$ and $ BC = 2x + 19$ Find $AC$.
A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {5x + 1} = {2x + 19}$ Solve for $x$ $ 3x = 18$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 5({6}) + 1$ $ BC = 2({6}) + 19$ $ AB = 30 + 1$ $ BC = 12 + 19$ $ AB = 31$ $ BC = 31$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {31} + {31}$ $ AC = 62$